The present invention relates to digital filtering, and in particular to digital filter design.
Some digital signal processing algorithms are based on filter design in the frequency domain. Typical applications are noise suppression algorithms for speech enhancement (see [1, 2]) and non-linear processors for echo cancellation. These filters are often quite long, which means that it may be desirable to perform the convolution (filtering) in the frequency domain, since this is less complex than convolution in the time domain. Since the input signal to be filtered is typically much longer than the filter, the desired linear convolution has to be implemented by circular sectioned or block convolution (see [3]) in order to avoid unacceptable delays and/or complexity.
A problem with filters designed in the frequency domain is that they are real-valued, which leads to a time domain representation in which the peak of the filter is split between the beginning and end of the filter (this is equivalent to a filter that is symmetric around lag 0, i.e. an non-causal filter). This makes the filter unsuitable for circular block convolution, since such a filter will generate temporal aliasing. This problem may be mitigated (but not eliminated) by weighting the data with a window that spans more than one block (see [2]). However, this will introduce a delay of 1 block, which is undesirable. The split peak also makes the filter unsuitable for time domain convolution, since the important parts of the filter are at the beginning and end of the filter. This makes it difficult to approximate the filter with a shorter filter to reduce the complexity of the time domain convolution.
Reference [4] describes a method that starts with an initial reduced length discrete frequency filter response (using either the Barlett or Welch method). The reduced length filter response is transformed to the time domain using a reduced length IDFT, circularly shifted to obtain a linear phase filter, zero-padded to obtain an extended length to avoid temporal aliasing, and transformed back to the frequency domain using an extended length DFT. A drawback of this method is that the resolution in frequency is reduced due to the initial reduced length filter.